6*. An Introduction to Number Theory CIS 5371 Cryptography 6*. An Introduction to Number Theory

Congruence and Residue classes Arithmetic modulo n, Zn Solving linear equations The Chinese Remainder Theorem Euler’s phi function The theorems of Fermat and Euler Quadratic residues Legendre & Jacobi symbols

   

Solving linear equations  

The Chinese Remainder Theorem

The Chinese Remainder Theorem

Example

Example

Euler’s phi function

The theorems of Fermat and Euler  

Legendre & Jacobi symbols

Legendre & Jacobi symbols

Legendre & Jacobi symbols

Example